I. INTRODUCTION

Corona quenching occurs when highly concentrated aerosols enter into an electrostatic precipitator (ESP). The current uptake drops dramatically and at the same time, the emission of particles goes up and sparking oc-curs. Usually, corona quenching is seen as a disturbance of regular electrostatic precipitator operation. Here we discuss corona quenching as a special (and very efficient) regime of ESP operation, which however requires special rules of design and operation.

II. THE ELECTRIC FIELD IN AN ESP UNDER

CONSIDERATION OF PARTICLE ATTACHED SPACE CHARGE

The knowledge of the local electric field E (V/m) in an ESP is fundamental for calculating particle charging kinetics and particle migration velocity. In common one stage ESPs, the electric field is, at least beyond a certain distance from the corona electrodes, mainly governed by the space charge in the ESP. For the axial-symmetric case of a tube wire type ESP (tube diameter rt (m), wire diameter rw (m)), the distribution of the electric field can be calculated, when a constant particle attached space charge density ρip (C/m³) is assumed over the ESP’s cross-section.

Assuming additionally a constant electrical mobility of the ions Zi (m²/(Vs)) while travelling from the corona wire to the collecting electrode and the applicability of the continuity equation for the ionic current (the loss of ions due to particle charging is discussed later) one finds the local ion space charge density ρi (C/m³) to depend on

the radius coordinate r (m) as follows [7]:

12

2

12

1

0

221

w

wiponset

ipiw

onsetipiw

ip

r

rrE

I

LZrexp

EI

LZr

LambertW

(1)

Here, I/L(A/m) is the current uptake per meter of co-rona wire, Eonset (V/m) is the Corona onset field strength and ε0 is the permittivity of the vacuum (As/(Vm)). The use of the <-1-branch of the LambertW-function is indi-cated by the index -1.

The corresponding electric field distribution is found to be: rE

(2)

For a given voltage U (V) applied to the ESP, the ion-ic current I in eqs. 1 and 2 has to be found iteratively by numerical integration of the electric field, where the cor-rect I fulfils the condition

(3)

i r

12

2

12

12

0

221

w

wiponset

ipiw

onsetipiw

ipi

r

rrE

I

LZrexp

EI

LZr

LambertWrLZ

I

rt

rwEdrU

Electrostatic Precipitator Operation at Corona Quenching Conditions – Theory, Simulation and Experiments

C. Luebbert and U. Riebel

Chair of Particle Technology, Brandenburgische Technische Universität Cottbus, Germany

Abstract—Mathematical models of different complexity are developed for the description of the residence time de-

pendent current uptake in a tube wire type electrostatic precipitator under conditions of corona-quenching. For a simple tube-wire geometry, corona quenching by concentrated aerosols is studied theoretically, by numerical simulation and ex-periments. The numerical simulations are executed in 1 D, whereby various levels of complexity (including particle and ion space charge, ion extinction, lateral mixing (turbulent diffusion), particle charge and size distribution, charging and agglome-ration kinetics) are attained. Simulation predictions of the current uptake behaviour are compared to experimental results from batch type and contin-uously operated electrostatic precipitators.

Keywords—electrostatic precipitation, corona quenching, space charge, ion yield, optimization

Corresponding author: Ulrich Riebel e-mail address: riebel@tu-cottbus.de Presented at the 12th International Conference of Electrostatic Precipitation, ICESP, in May 2011 (Nuremberg, Germany)

196 International Journal of Plasma Environmental Science & Technology, Vol.5, No.2, SEPTEMBER 2011

In combination with particle charging and deposition models, (1)- (3) allow a stepwise calculation of the whole deposition process including the effect of particle space charge on ion and electric field distribution. Based on the assumption of fast lateral mixing and hence constant par-ticle concentration and charge over the ESP’s cross-section, an average gain in particle charge can be calcu-lated from local charging kinetics. In combination with the deposition loss of charged particles that can easily be calculated from known particle electrical mobility and field strength at the surface of the collecting electrode, the rate of change in average particle charge, particle concentration and particle attached space charge concen-tration can be calculated.

The result of this calculation method is compared to other model predictions in Fig. 5. However this calcula-tion procedure is already quite complex. III. PARTICLE DEPOSITION IN THE STRONGLY QUENCHED

REGIME

In case of very high particle concentration, the local current uptake level can be in the sub percent rage of the clean gas current. Therefore, in the case of strong quenching, it is justified to neglect the contribution of the ionic space charge to the electric field.

In this case the drop of the electric potential ΔU(V) over the particle attached space charge has to be equal to the difference between the applied voltage and the corona onset voltage Uonset (V). In this limiting case we find the electric field to be

(4)

The space charge density which causes the drop of

the electric potential between the corona wire and the tube is then found to be [1, 3]:

(5)

where e (As) is the elementary charge, n the number of charges per particle and c(m-3) the particle number con-centration.

Hence the particle number concentration c (1/m³) can be expressed by the average particle charge n in the quenched regime.

(6)

For a monodisperse aerosol one can derive a constant

particle deposition rate dc/dt (1/m²s) based on the diffe-rential Deutsch-Anderson approach:

(7)

Here, V (m³) is the tube volume, A (m²) is the surface

of the collecting electrode, wsed (m/s) is the drift velocity of the particles at the surface of the collecting electrode, Cu (-) is the Cunningham slip correction factor, x (m) is the particle diameter and η is the gas viscosity (Pa s).

Solving this equation for dc/dt, writing A/V=2/r for a tube, and substituting c n e by (5) and E(r) from (4), one finds the constant particle deposition rate in the strongly quenched regime [1, 3]:

(8)

Departing from the deposition rate and the initial aer-

osol concentration, we can derive a rough estimate of the residence time needed to overcome the quenched state (see Fig. 5).

If additionally the limitation of the electric field by an excessive sparking frequency is considered, one can use (8) for maximizing the deposition rate.

For example, a corona wire with 1mm diameter is chosen. The corresponding onset electric field is calcu-lated by the Peek [5] formula. With the maximum aver-age field U/r assumed to be 600 kV/m (typical value for dense sulphuric acid mist as given by Parker [4]) and the maximum electric field at the collecting electrode limited to 800kV/m, one finds tube diameter dependent deposi-tion rates as shown in Fig. 1. The optimum tube diameter is found to be around 50 mm, independently of aerosol characteristics.

w

t

onset

t

r

rlnr

U

r

UrrE

2

2

204

t

p,ir

Ucne

2

04

tner

Uc

tsed rEx

neCucAcAw

dt

dcV

3

w

t

onset

t

r

rlnU

U

x

Cu

r

U

dt

dc2

3

84

20

Fig. 1. Particle deposition rate divided by the particle mechanical

mobility B (m/(Ns)) as a function of the tube radius. Wire diameter: 1mm. Sparking criteria as described in text.

197Luebbert et al.

IV. PARTICLE CONCENTRATIONS WHICH INDUCE STRONG

QUENCHING

The continuous deposition of charged particles (8) while the particle attached space charge is assumed to be constant (5), implies that the charge per particle must increase with time. Therefore a certain ion concentration and hence an ionic current must be present even in the strongly quenched regime.

For small currents, where the assumption of a negli-gible contribution of the ionic space charge is still justifi-able, one can derive the time dependent current uptake from a balance of the particle attached space charge.

As the particle space charge concentration is assumed to be constant in the quenched regime (5) it follows that the losses of particle space charge have to be compen-sated by an increase of average particle charge

(9)

And hence

(10)

whereby the particle deposition rate on the right hand side can be substituted by (8).

The gain of the average particle charge can calculated from an ion extinction function, if fast radial mixing and therefore constant particle concentration and average particle charge over the ESP’s cross-section is assumed.

(11)

whereby the ion-particle combination coefficient Λ (m³/s) equals the particle charging rate in coulombs per second divided by the local ion space charge density. Λ /(ZiE) (m²) can be interpreted as the effective ion trap-ping cross section of a particle.

The difference between the ionic current at the wire and at the precipitation electrode is the current which is attached to the particles and leads to the increase of mean particle charge. So we find

(12)

Using (12) for the left hand side of (10) and the parti-cle deposition rate in the quenched regime multiplied by the average particle charge for the right hand side, the ionic current uptake per meter of corona wire is the only unknown parameter. Substituting the concentration c by (6), the solution of the resulting equation yields the spe-cific current uptake:

rt

rwit

w

tonset

tw

drrEZner

Uexp

Ur

rlnUU

xr

neCu

L

rI

20

21

20

41

23

8

(13) Equation (13) also allows to calculate the transmis-

sion of the ion current through the aerosol during the precipitation process. Fig. 2 shows the ion transmission as a function of the average particle charge.

Of course, (13) holds true only in the strongly quenched regime where ionic space charge is negligible. Therefore we define the strongly quenched regime to be restricted to current uptakes of less than five percent of the clean gas current. Fig. 3 shows the current uptake as a function of average particle charge as calculated by (13) for Λ calculated by different charging theories.

A correlation between average particle charge and residence time t(s) can be found from an integration of the deposition kinetics, whereby the concentration c(t) is substituted by (6) and c0 (1/m²) is the inlet concentration of the particles

(14)

The combination of (13) and (14) allows the calcula-tion of the residence time dependent specific current up-take as shown in Fig. 4. A comparison to other calcula-tion methods is given in Fig. 5.

V. SIMULATIONS

Compared to the more or less analytical models pre-sented above, numerical calculations additionally allow for the consideration of particle size distribution and dis-tribution of particle charge within each size fraction.

0dt

dcne

dt

dnce

dt

d p,i

dt

dcn

dt

dnc

rw

rti

wt drrEZ

cexprIrI

rt

rwit

w drrEZ

cexp

Ler

rI

dt

dnc 1

2

Ur

rln

UU

ner

Ucr

Cu

x

nt

wire

tube

onset

tube

tube

2

116

43

20

20

04

Fig. 2. Ion transmission through a 200nm aerosol (εr=2.1) in an ESP. Tube diameter: 0.2m, corona wire diameter 0.2mm, applied voltage

40kV. Λ according to Lawless [2] charging model.

198 International Journal of Plasma Environmental Science & Technology, Vol.5, No.2, SEPTEMBER 2011

Assuming negligible axial dispersion and radial symmetry of the system, the problem can be treated as 1-dimensional on the radius coordinate, while parameters are changing with time. The basic equations to be solved in a simulation are:

1) Equation of continuity for the ionic current, modi-

fied for ion losses due to particle charging.

PC

j

CC

k k,j,extk,j Aciidiv1 1

(15)

whereby i (A/m²) is the current density and

(16)

Here PC is the number of particle size classes and CC is the number of charge classes. 2) Poisson’s equation

(17)

3) Electric potential

(18)

4) Particle charging kinetics

(19)

5) Particle motion/-deposition (class-wise)

, , , , (20) Here, j (1/(m²s)) is the particle flux density and Ddisp (m²/s) is the turbulent diffusion coefficient.

For comparison of experimental and theoretical time dependent current uptake, the particle size distribution was discretized logarithmically into eight size fractions, the particle charge distribution within each size fraction was resolved down to one elementary charge and the radius was discretized linearly into 50 elements. A simu-lation for a monodisperse aerosol is show in Fig. 5 in comparison to the simpler models.

Altogether, these simulations are quite complex and probably, the analytical model prediction may be suffi-cient for design and trouble shooting in many cases.

rEZ

rA

i

k,jk,j,ext

0 p,iiEdiv

gradE

kji

kj edt

dn,

,

Fig. 3. Average charge dependent current uptake according to (14) for

different charging models. Aerosol and ESP as described in Fig. 2.

Fig. 4. Residence time dependent current uptake for data as used in Fig. 3 and an initial number concentration of c0=3·1014m-3. Clean gas current

1,1mA/m.

Fig. 5. Current uptake as a function of the residence time by the as-

sumption of a complete deposition under quenched conditions (fat solid line), by combination of (13) and (14) (short dashes), by the stepwise

calculation using (1), (2) and (3) for calculation of ion and electric field distribution (long dashes), and by simulation (thin full line). Geometrical

parameters of the ESP as in Fig. 2, applied voltage 20kV, particle diameter 200nm (εr=2.1), initial number concentration 1014 m-3.

199Luebbert et al.

VI. EXPERIMENTAL VALIDATION OF THE MODEL

A first series of experiments was carried out in an ESP that is operated in batch mode (see Fig. 6). This ESP consists of two tube-wire type ESPs in parallel, which are connected on the top and bottom side. Each of these ESPs has a tube diameter of 0.2m and a wire diameter of 0.2mm. The total length of each ESP is 1.6m. To ensure well mixed conditions, fans were inserted into the con-necting pieces between the two ESPs. They provide a circulating gas flow velocity of approximately 5m/s and maintain well mixed conditions.

The current uptake is measured from one of the two cylindrical sections by a digital recording oscilloscope via a 10 kΩ resistor. Sample points for the particle at-tached space charge density, measured by an FCE, and the particle size distribution and concentration by SMPS are located at the other tube.

As an aerosol, a condensation aerosol of liquid paraf-fin was used.

For the positive corona the onset voltage was found to be 8.0 kV. The clean gas current voltage curve is in ex-cellent agreement with theoretical predictions [6] when the ion mobility is set to 1.55cm²/Vs.

The predicted space charge density in the quenched state (see (2)) is compared to measurement results in Fig. 7. For measurement of the time dependent current uptake, the ESP was flushed with aerosol. Particle size distri-bution and concentration is measured by SMPS while flushing. When sampling was finished, the ESP was switched to the batch mode by closing the aerosol in- and outlet. The voltage was switched on and the current was sampled as function of residence time. The current up-take characteristics for different applied voltages are compared to simulation predictions in Fig. 8.

The residence time for which the current approaches five percent of the clean gas current is compared to the prediction of the analytical model in Fig. 9. For lower operation voltages and hence longer residence time, it appears that the coagulation of uncharged particles has to be accounted for.

To show the transferability of the findings to common continuously operated ESPs, the current voltage curve of a continuously operated ESP was measured under the influence of high particle concentration. The results are shown in Fig. 10 in comparison to the residence-time averaged currents according to the analytical model and simulations.

Fig. 6. Experimental setup for measurement of the time dependent

current uptake.

Fig. 7. Comparison of measured and predicted space charge density in the quenched regime.

Fig. 8. Time dependent current uptake per length of corona wire for

different applied voltages in comparison to simulations. Aerosol: liquid paraffin, εr=2.1, c0=4.3·1013m-3, CMD: 210nm, GSD: 1.4.

200 International Journal of Plasma Environmental Science & Technology, Vol.5, No.2, SEPTEMBER 2011

VII. CONCLUSION

Analytical models are able to describe current uptake

and particle deposition quite well for strong corona quenching and allow to optimize the dimensioning of wire-tube ESPs for quenched operation. With a 1D simu-lation, the transition from the quenched state to un-quenched operation can be modelled with very good ac-curacy.

ACKNOWLEDGEMENT This project was supported by ELSTATIK Stiftung

Guenter und Sylvia Luettgens, Odenthal, Germany, which is gratefully acknowledged.

REFERENCES [1] P. Cooperman, “Dust space charge in electrostatic precipitation”

(single volume journal), IEEE Trans. Comm. Elect., vol. 82, pp. 324-326 ,1963

[2] P. A. Lawless, “Particle charging bounds, symmetry relations and analytic rate model for the continuum regime” (journal article) J. Aerosol Sci., vol.27, no. 2, pp. 191-215, 1996

[3] S.Matts, L. Lindau, “Some space charge problems encountered with large electrode spacing” (Conference Proceeding) , Proceedings of the Second International Conference on Electrostatic Precipita-tion,(Kyoto, Japan), pp. 911-919, 1984

[4] K. Parker, “Applied Electrostatic Precipitation” (Book),

Springer, 1996

[5] F. W. Peek, “Dielectric Phenomena in High Voltage Engineering” (Book), McGraw-Hill, 1929

[6] H.-J. White, “Industrial Electrostatic Precipitation” (Book)

Addison-Wesley Publ. Co., 1963

[7] Ch. Luebbert, “Zur Charakterisierung des gequenchten Zustands im Elektroabscheider bei hohen Aerosolkonzentrationen ” (submitted as doctoral thesis), BTU Cottbus, 2011.

Fig. 9. Quenched residence time according to the current uptake

measurements in Fig. 8 and prediction of the quench time by the analyti-cal model with and without consideration of thermal coagulation. The

CMD was used as particle size in the analytical model.

Fig. 10. Clean gas current voltage curve and current voltage curve underthe influence of particle space charge for a continuously operated ESP.

201Luebbert et al.